Solve Using the Quadratic Formula 5m^2+3m=7

$5 m^{2} + 3 m = 7$

Step 1

Subtract $7$ from both sides of the equation.

$5 m^{2} + 3 m - 7 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 5$ , $b = 3$ , and $c = - 7$ into the quadratic formula and solve for $m$ .

$\frac{- 3 \pm \sqrt{3^{2} - 4 \cdot (5 \cdot - 7)}}{2 \cdot 5}$

Step 4

Simplify.

Simplify the numerator.

Raise $3$ to the power of $2$ .

$m = \frac{- 3 \pm \sqrt{9 - 4 \cdot 5 \cdot - 7}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 7$ .

Multiply $- 4$ by $5$ .

$m = \frac{- 3 \pm \sqrt{9 - 20 \cdot - 7}}{2 \cdot 5}$

Multiply $- 20$ by $- 7$ .

$m = \frac{- 3 \pm \sqrt{9 + 140}}{2 \cdot 5}$

Add $9$ and $140$ .

$m = \frac{- 3 \pm \sqrt{149}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$m = \frac{- 3 \pm \sqrt{149}}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$m = \frac{- 3 \pm \sqrt{149}}{10}$

Decimal Form:

$m = 0.92065556 \dots, - 1.52065556 \dots$